Here's what I think she's thinking:

"I'm firmly resolved not to be Lucy's rival, but she probably regards me as a rival because I botched some parts of our earlier conversation. She'll make things more uncomfortable for me if she continues to mistake me for a rival."

Here's a big juicy botch, from chapter 22:

"... Though you do not know him so well as me, Miss Dashwood, you must have seen enough of him to be sensible he is very capable of making a woman sincerely attached to him."

"Certainly," answered Elinor, without knowing what she said; ...